The Museum of Contemporary Art (MOCA) is a fun way to spend an afternoon in Taipei. It's not a particularly big museum which means museum fatigue is less likely to happen, crowds are spread across the different rooms and it never felt crowded or difficult to view the artworks on display. While the exhibitions are contemporary in nature, I thought they were shown in an accessible manner with each individual artwork able to stand alone and entertain the viewer.
On weekends, you will probably find a plethora of activities happening around MOCA. When I visited, there was a flea market happening and it was fun to browse the stalls set up mostly by students selling their wares and second-hand clothes.